Can I insulate the underside of my first-floor fireplace chase? I would like to put batt-insulation, and a ceiling below the fireplace. I currently use the area as a storage closet. The area is very cold, and the air seems to migrate upstairs. I also get frost above the basement wall, on the framing. The fireplace is ~20 years old, and non-gas.
You’ll need to check on the installation requirements for your specific type of pre-fabricated fireplace. They must be installed per specific installation requirements. In general, they require clearance around the metal firebox, and around the metal flue that is routed up through the boxed-in chimney chase. I don’t think your real problem is in the basement. I think the real problem is the exterior wall behind the fireplace. Insulating below the floor will be of little value.
The areas around the fireplace can be a big heat-loss, because the outside wall behind the fireplace may not be properly insulated. The exterior wall should be framed so that it can be insulated and sealed like a typical exterior wall. This does not always happen when the wall is buried behind a manufactured fireplace, and brick facing.
The area below the fireplace (above the foundation wall) should be independent from the fireplace installation. Ice in this area (and around the sill/band joist) occurs because air moves through the fiberglass batts, and moisture condenses on the cold surface.
The ideal fix at the top of the foundation wall is to have the area sealed and insulated with spray foam. This will seal the air-leaks, provide a vapor-barrier, and insulate the area.
If you want to work with fiberglass, you need to remove it and caulk any gaps in the area around the sill-plate to the sub-floor. Fill the space with tight-fitting fiberglass, then seal it with drywall and plastic caulked in place on the heated side. It sounds like the foam is a much better option.